Copyright ©2011 Brooks/Cole, Cengage Learning Relationships Between Categorical Variables – Simpson’s Paradox Class 27 1

Homework Check Assignment: Chapter 4 – Exercise 4.1 and 4.7 Reading: Chapter 4 – p

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Homework Check Assignment: Chapter 4 – Exercise 4.15, 4.17 and 4.29 Reading: Chapter 4 – p

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Copyright ©2011 Brooks/Cole, Cengage Learning 9 Misleading Statistics About Risk Questions to Ask: What are the actual risk? What is the baseline risk? What is the population for which the reported risk or relative risk applies? What is the time period for this risk?

Copyright ©2011 Brooks/Cole, Cengage Learning 10 Example 4.7 Case Study 1.2 Revisited: Disaster in the Skies? Look at risk of controller error per flight: In 1998: 5.5 errors per million flights In 1997: 4.8 errors per million flights “Errors by air traffic controllers climbed from 746 in fiscal 1997 to 878 in fiscal 1998, an 18% increase.” USA Today Risk of error increased but the actual risk is very small when it is compared to the actual number of the risk..

Copyright ©2011 Brooks/Cole, Cengage Learning 11 Example 4.8 Dietary Fat and Breast Cancer Two reasons info is useless: 1.Don’t know how data collected nor what population the women represent. 2.Don’t know ages of women studied, so don’t know baseline rate. “Italian scientists report that a diet rich in animal protein and fat – cheeseburgers, french fries, and ice cream, for example – increases a woman’s risk of breast cancer threefold.” Prevention Magazine’s Giant Book of Health Facts (1991, p. 122).

12 Example 4.8 Dietary Fat and Breast Cancer (cont) Age is a critical factor. Accumulated lifetime risk of woman (currently 30) developing breast cancer by certain ages: By age 40: 1 in 227 By age 50: 1 in 54 By age 60: 1 in 24 By age 90: 1 in 8.2 Annual risk: only 1 in 3700 for women in early 30’s. If Italian study was on very young women, the threefold increase in risk represents a small increase – that is 3 in 3700.

Copyright ©2011 Brooks/Cole, Cengage Learning 13 Simpson’s Paradox The effect of a confounding factor is strong enough to produce a paradox, e.g., the direction of a relationship or difference is reversed within subgroups compared to direction within the whole group. How? A combination of differing sample sizes within the subgroups and differing magnitudes of response variable summaries.

Copyright ©2011 Brooks/Cole, Cengage Learning 14 Example 4.11 Blood Pressure and Oral Contraceptive Use Hypothetical data on 2400 women. Recorded oral contraceptive use and if had high blood pressure. Percent with high blood pressure is about the same among oral contraceptive users and nonusers.

Copyright ©2011 Brooks/Cole, Cengage Learning 15 Example 4.11 Blood Pressure and Oral Contraceptive Use (cont) Many factors affect blood pressure. If users and nonusers differ with respect to such a factor, the factor confounds the results. Blood pressure increases with age and users tend to be younger. In each age group, the percentage with high blood pressure is higher for users than for nonusers  Simpson’s Paradox.

Copyright ©2011 Brooks/Cole, Cengage Learning The Effect of a Third Variable and Simpson’s Paradox Example 4.9 Sleep-Time Lighting, Child Vision, and Parents’ Vision Children who slept with some light in room before age of 2 had a higher incidence of nearsightedness later in childhood than those who slept in complete darkness.

Copyright ©2011 Brooks/Cole, Cengage Learning 17 Example 4.9 Sleep-Time Lighting, Child Vision, and Parents’ Vision Parental vision could be a confounding variable that affects child’s vision and type of nighttime lighting used. Two later studies found nearsighted parents more likely to use a nightlight than parents with good vision.

Homework Assignment: Chapter 4 – Exercise 4.32 and 4.33 Reading: Chapter 4 – p